The Jacobi last multiplier, Lagrangian and Hamiltonian for Levinson–Smith type equations

Abstract

We derive the Jacobi last multiplier for second-order ordinary differential equations of the Levinson–Smith type by using a combination of previous techniques employed for the Liénard-I and II classes of equations. This opens up the possibility for a Lagrangian or Hamiltonian description of the systems governed by the Levinson–Smith type of equations as well as simplifying the problem of finding first integrals of motion. The procedure has been illustrated by a number of suitable examples alongwith Kamke's equation with explicit time dependent coefficients.